A conducting rod of length l is moving in a transverse magnetic field of strength B with veocity v. The resistance of the rod is R. The current in the rod is

Options

A. `(Blv)/(R)`
B. Blv
C. zero
D. `(B^(2)v^(2)l^(2))/(R)`

Answer

To find the current in a conducting rod of length \( l \) moving in a transverse magnetic field of strength \( B \) with velocity \( v \), we can follow these steps:

### Step 1: Understand the Concept of Electromagnetic Induction
When a conducting rod moves through a magnetic field, an electromotive force (EMF) is induced in the rod due to electromagnetic induction. This is described by Faraday's law of electromagnetic induction.

### Step 2: Calculate the Induced EMF
The induced EMF (\( E \)) in the rod can be calculated using the formula:
\[ E = B \cdot l \cdot v \]
where:
- \( B \) is the magnetic field strength,
- \( l \) is the length of the rod,
- \( v \) is the velocity of the rod.

### Step 3: Relate EMF to Current
The current (\( I \)) induced in the rod can be calculated using Ohm's law, which states:
\[ I = \frac{E}{R} \]
where \( R \) is the resistance of the rod.

### Step 4: Substitute the Induced EMF into the Current Formula
Substituting the expression for EMF into the current formula gives:
\[ I = \frac{B \cdot l \cdot v}{R} \]

### Conclusion
Thus, the current in the rod is:
\[ I = \frac{B \cdot l \cdot v}{R} \]

### Final Answer
The current in the rod is \( \frac{B \cdot l \cdot v}{R} \).